Children's arithmetic development : contributions of symbolic and nonsymbolic magnitude comparison

• Main Author: Watson, Sarah Elizabeth
• Other Authors: Goebel, Silke
• Published: University of York 2013
• Subjects: 150
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595091

This thesis aimed to explore the predictors of children’s arithmetic development with a specific focus on magnitude comparison. Children were assessed in whole class groups in order to recruit a sample large enough to use structural equation modeling (Chapters 2, 4 and 5), while also assessing a subsample of children individually with computerised measures (Chapter 6). This thesis also aimed to explore children’s development on the magnitude comparison tasks within the same group of children (Chapters 3 and Chapter 6 Study 1). Chapter 2 first assessed the underlying latent factors that different comparison tasks may have in common. It was found that symbolic and nonsymbolic comparison tasks loaded on the same factor (magnitude comparison), whilst letter comparison formed a separate factor. Furthermore, children’s magnitude comparison ability was found to be a concurrent predictor of their arithmetic achievement but letter comparison was not. The longitudinal analyses in Chapters 4 and 5 show how magnitude comparison ability was not a predictor of children’s untimed arithmetic ability, or fluency at completing subtraction and multiplication problems either one or two years later. However, it was a significant predictor of addition fluency one year later. In comparison, number identification ability was found to be a consistent predictor of arithmetic achievement both concurrently and longitudinally. Chapter 6 investigated whether the inconsistent findings regarding the importance of magnitude comparison ability was due to the methodology used to assess it. Computerised magnitude comparison tasks more akin to those in previous studies were individually presented to a subgroup of children that also completed the group based measures. Neither symbolic nor nonsymbolic comparison ability was found to predict later arithmetic achievement, whereas number identification was a significant predictor. Finally in Chapters 3 and 6, it was found that children improved significantly over time on all of the magnitude comparison tasks presented.